Doing some simple maths on a the simple model of a (lossless) double tuned
vertical I got this result :
1. Starting from a (lossless) single tuned vertical you get
+------+
| |
+-+ ----- where L = loading coil
L | | ----- C C = antenna capacitance
| | | R = radiation resistance
+-+ +-+ R Z = antenna impedance
| | |
-----+ +-+
Z = |
------------+
If the reactance L (XL) cancels the reactance of C (XC) the antenna
impeadnce Z equals the radiation resistance R
so wL = 1/(wC) (where w = 2 x Pi x frequency)
2. 'Upgrade' the antenna to a double tuned vertical :
+------+--------+
| | |
+-+ ----- +-+
L' | | ----- C | | L'
| | | | |
+-+ +-+ R +-+
| | | |
-----+ +-+ |
Z = | |
------------+--------+
Instead of 1 inductor L we now have 2 inductors L' of the double value (2L)
Since the values of C and R are unchanged is wL' = 2/(wC)
Further XC = 1/(jwC) = -j/(wC) (where j = square root of -1)
and XL' = jwL' = j2/(wC) = -2XC
Calculating Z gives
Z = XL + (XL x (XC + R)) / (XL + XC + R) -> extract XL
Z = XL x (1 + (XC + R) / (XL + XC + R)) -> replace XL by -2XC
Z = -2XC x (1 + (XC + R) / (-2XC + XC +R)) -> -2XC + XC = -XC
Z = -2XC x (1 + (XC + R) / (R - XC)) -> equalize to (R-XC)
Z = -2XC x (R - XC + XC + R) / (R - XC) -> R - XC + XC + R = 2R
Z = -2XC x (2R) / (R - XC)
for practical antennas will XC be in the range of 500 to 5000 Ohm while R
will be well below 1 Ohm so we can say that R - XC = -XC
Z = -2XC x (2R) / (-XC) -> -2XC / -XC = 2
Z = 4R
So the antenna impedance of a resonant double tuned vertical will be 4
times the impedance of a single tuned vertical.
But what to do with the 'loss resistance' (RL) in the real world ?
Assume a simple model where both tuned sections share the same
ground-system. In that case RL would be in series with R and this would
mean that a double tuned vertical would not only quadruple the radiation
resistance but also the loss resistance, resulting in an unchanged ratio
between radiation resistance and loss resistance.
From the above I expect that a multiple-tuned vertical will only outperform
a simple vertical if each tuned section has at least its own independent
groundsystem. This would also mean that you need a certain distance between
the tuned sections in order to get these independent grounds.
Comments welcome ...
73, Rik
So
Rik Strobbe ON7YD
[email protected]
Villadreef 14 B-3128 Baal BELGIUM (JO20IX)
| 